Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
370 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #476 |
| commutator, Frattini, cosocle | C22×C8 | C23×C71 |
| prime radical | C2×#135×C71 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C22×C4×C71 ◁ C2×C4×C8×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#499×C71 | C2 | semidirect |
| 4. C71×#1383 | C2 | semidirect |
| 5. C71×#1376 | C2 | semidirect |
| 109. #13372 | C71 | direct (N × H) |
| 115. C2×#499 | C2×C71 | semidirect |
| 118. #1383 | C2×C71 | semidirect |
| 119. #1376 | C2×C71 | semidirect |
| 120. C71 | #13372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#499×C71 | 2 |
| C2×#360×C71 | 2 |
| C71×#1974 | 2 |
| C71×#1383 | 2 |
| C71×#1376 | 2 |
| #13372 | 71 |